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"shows a constant" is correct and usable in written English.
You can use it to describe a situation when something remains the same throughout a period of time, such as a behavior, attitude, or quality. For example, "The study reveals that attendance at the event shows a constant trend over the past 5 years."
Exact(50)
A study in historical perspective that shows a constant expansion of free-speech rights.
Mr. Rivette shows a constant tendency to move backward, to find the ultimate context, and that has often come close to a wish to include, or allude to, the way the whole enterprise is being filmed.
Figure 6 shows a constant offset between simulations and measurements.
The global combustion intensity shows a constant value within uncertainty limits for flames with CO2 addition.
The Home home screen experience is focused on Cover Feed, which shows a constant stream of full-screen photos and stories you can just sit back and watch.
Comparing the average energy demand for each sector shows a constant high demand level in the manufacturing sector.
Similar(10)
It was flat, showing a constant level of importance.
His subsequent development showed a constant refinement of his vision.
"The thought of showing a constant yesterday – a palimpsest of time, if you like – is a happy one," he reflects.
Yet every time she combed her hair or brushed her teeth, the mirror showed a constant reminder of the brutality.
"We're showing a constant presence," she said, "and now we're bringing people who are specialists".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com